Error analysis of the reproducing kernel particle method

By Weimin Han, Xueping Meng. 2001

199 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/35b293b7c782373ed50a5845307e743ecd59acd7

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

On Approximation in Meshless Methods (2005, background): “Variants can be found, for example, in [55,41,1].”
Least squares moving particle semi-implicit method (2014, result): “It must be mentioned that the definition of (re, p)regularity above is nearly accordance with the concept of ( , p)-regularity, which has been introduced by Han and Meng [34] for the RKPM. Definition 3.4 (Admissible particle distribution on the standard LSMPS scheme type-A) For a given particle dist”
A reproducing kernel method with nodal interpolation property (2003, methodology): “For details, see Reference [23].”
Positivity conditions in meshless collocation methods (2004, methodology): “The regularity of the point distribution [17] implies that, in a cloud, the points are distributed in such a way that the moment matrix is non-singular.”
A level set enhanced natural kernel contact algorithm for impact and penetration modeling (2015, background): “1 It has been shown that the support size of the RK shape function affects the accuracy of the approximation [46], where larger normalized support size yields better solution accuracy while consuming higher CPU.”
Reproducing kernel element method Part II: Globally conforming Im/Cn hierarchies (2004, methodology): “This new technology is now termed as reproducing kernel element method (RKEM) (see Part I), which is in contrast to the early meshfree reproducing kernel particle method (RKPM) [12,17–19,21,22].”
MLS (moving least square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement (2007, unknown): “This theorem was extended, by Han and Meng [23,24] to the case of the multi-dimensional domain wherein only linear polynomials are employed for the bases.”
Truncation error in mesh‐free particle methods (2006, unknown): “Han and Meng [26] have shown theoretically that error in RKPM is of order h p +1 for certain classes of particle distribution and data function, where p is the highest order of polynomial function to be reproduced exactly.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “The convergence of the Galerkin meshfree method using MLS/RK/PU approximation with p th order completeness has been shown to be (Chen et al. 2003; Han and Meng 2001; Liu et al. 1996a, 1997c) where a is the maximum support dimension of the approximation functions; and C is independent of a and p .”
A generalized approximation for the meshfree analysis of solids (2011, background): “Bounding the Lebesgue function in the non-convex GMF approximations, such as the MLS and the RK approximations, is more involved and limited to certain conditions [36].”